Stability analysis of predictor based least squares algorithm and finite precision arithmetic error effects

The numerical property of the recursive least squares (RLS) algorithm has been extensively studied. However, very few investigations are reported concerning the numerical behavior of the predictor based least squares (PLS) algorithms that provide the same least square solutions as the RLS algorithm. This paper studies the numerical property of the backward PLS (BPLS) algorithm. First, the stability of the BPLS algorithm is verified by using the state space method. Then, finite-precision arithmetic error effects on both the BPLS and the RLS algorithms are presented through computer simulations. Some important results are obtained, which demonstrate that the BPLS algorithm appears quite robust to round-off errors and provides a much more accurate and stable numerical performance than that of the RLS algorithm under finite-precision implementation